This study addresses cumulative damage and its evolution during the cold dwell fatigue of a near-α titanium alloy. An experimental study was undertaken to examine the evolution of life, strain, strength and damage of 13 titanium IMI 834 samples cut from a single disk forging. The samples were tested in the same dwell-fatigue loading conditions. In the dwell phase, the load is maintained at 80% of ultimate tensile strength (824 MPa, 90% of yield strength) for 30 s. The secant Young’s modulus and inelastic strain at minimum load were measured in order to document the evolution of the irreversible damage against the number of cycles for all specimens. Experimental observations show significant differences in dwell-fatigue life and damage behavior. This mechanical analysis and an analysis of the cumulative Weibull reliability distribution suggest a bimodal dwell-fatigue failure process. Some features of the mechanical behavior can be used to sort the samples according to each of the two failure modes and improve the reliability of the fatigue test campaign.